| F. Nielsen and M. Yvinec. An output-sensitive convex hull algorithm for planar objects. Technical Report 2575, Institut nationale de recherche en informatique at en automatique, INRIA Sophia-Antipolis, 1995. |
....: If the functions in H are linear, then the problem can of course be solved in linear time. Reichling [24] described a linear time algorithm for the quadratic case. The dual of the problem is equivalent to finding a bridge [16] of a convex hull of k planar convex objects. Nielsen and Yvinec [22] gave an O(k) time algorithm for the case when two objects may intersect at most a constant number of times. We know of no nontrivial deterministic algorithm for the general case. Chazelle and Matousek [7] specifically pointed out that their derandomization technique is not applicable to this ....
F. Nielsen and M. Yvinec. An output-sensitive convex hull algorithm for planar objects. Research Report 2575, INRIA, Sophia-Antipolis, France, 1995.
....Nielsen is no longer true in higher dimensions. For example, in dimension 2, we may have c (S) 3 2 b (S) 2. 2 Getting an output sensitive algorithm The methodology consists in grouping the intervals into groups and to preprocess each group in order to answer eOEciently queries [Cha95, NY95] Typically, our queries are of two kinds: iwhat are the intervals stabbed by a point p j and iwhich interval has the rightmost left endpoint j. Moreover, we must be able to remove some of these intervals at some steps. We use the interval tree of McCreight [McC80, PS85] as the data structure for ....
F. Nielsen and M. Yvinec. Output-Sensitive Convex Hull Algorithms of Planar Convex Objects. Research Report, INRIA, BP93, 06902 So phia-Antipolis, France, 1995.
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F. Nielsen and M. Yvinec. An output-sensitive convex hull algorithm for planar objects. Technical Report 2575, Institut nationale de recherche en informatique at en automatique, INRIA Sophia-Antipolis, 1995.
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